In medium bowl, stir together 1/2 cup of the flour, baking powder, beer and egg. Place 1/4 cup flour and coconut in two separate bowls.

Holding each shrimp by the tail, dredge in flour, them dip in beer batter; allow excess to drip off. Roll shrimp in coconut, and place on a baking sheet lined with wax paper. Refrigerate for 30 minutes.

Meanwhile, heat oil to 350F in a heavy pot or deep-fryer. Cook shrimp in batches, without crowding the pot or fryer; cook, turning once, for 2 to 3 minutes, or until golden brown. Using tongs, transfer shrimp to paper towels to drain. Serve warm with your favorite dipping sauce.